. y= Ax4 + Bx3 + Cx2 + Dx + E (a) Set up this problem as a system of linear equations. (b) Find the quartic polynomial that goes through these data points. (c) Use this polynomial to approximate the density 50% of the way out of the sun.

[W] Consider the following data from NASA about the density of the sun. 0 When you are 10% of the way out from the center of the sun (use .1: = 0.1), the density is approximately 82.9619 g/ 01113. I When you are 20% of the way out of the sun, the density is approximately 38.7504 g/em3. 0 When you are 70% of the way out of the sun, the density is apprOximately 1.7819 g/cm3. a When you are 80% of the way out of the sun, the density is approximately 1.9824 g/cm3. 0 When you are 90% of the way out of the sun, the density is approximately 0.7859 g/cm3. We want to use this data to nd a quartic (4th degree) interpolating polynomial for the density of the sun throughout. y=Am4+Bm3+sz+Dm+E (a) Set up this problem as a system of linear equations. (b) Find the quartic polynomial that goes through these data points. (c) Use this polynomial to approximate the density 50% of the way out of the sun